close

Вход

Log in using OpenID

embedDownload
Name: ____________________________________
Date: _________________
OTHER TYPES OF REGRESSION
COMMON CORE ALGEBRA I
In the last two lessons we fit bivariate data sets with lines of best fit. Sometimes, though, linear models are
not the best choice. We can fit data with all sorts of curves, the most common of which are linear,
exponential, and quadratic. But, there are many other types. Before we look at exponential and quadratic
regression, recall the general shapes of these two types of functions.
EXPONENTIAL AND QUADRATIC GRAPHS
EXPONENTIAL GRAPHS
QUADRATIC GRAPHS
Exercise #1: For each scatterplot shown below, determine if it is best fit with a linear, exponential, or quadratic
function. Draw a curve of best fit depending on your choice.
(a)
(b)
(c)
Type: ________________
Type: ________________
Type: _______________
Type: _________________
Type: ________________
Type: _______________
(d)
COMMON CORE ALGEBRA I, UNIT #10 – STATISTICS – LESSON #8
eMATHINSTRUCTION, RED HOOK, NY 12571, © 2013
Our calculators can produce equations for exponentials of best fit and quadratics of best fit (along with a lot
of other types of curves).
Exercise #2: Biologists are modeling the spread of flu cases as the spread around a particular city. The total
number of cases, y, was recorded each day, x, after the total first reached 16. The data for the first week is
shown in the table below.
x, days
0
1
3
64
6
7
y, cases
16
(a) Use your calculator to find the exponential
regression equation for this data set in the form
y  a b
x
18
22
25
33
35
(b) Based on the regression equation, how many
total cases of flu will there be after two weeks?
Round all parameters to the nearest
hundredth.
(c) According to your model, by what percent are
the flu cases increases on a daily basis?
(d) Hospital officials will declare an emergency
when the total number of cases exceeds 200.
On what day will they need to declare this
emergency?
So, really, regression, as mysterious as it may be, is all about finding the best version of whatever curve we
think fits the data best.
Exercise #3: The cost per widget produced by a factory generally drops as more are produced but then starts to
rise again due to overtime costs and wear on the equipment. Quality control engineers recorded data on the cost
per widget compared to the number of widgets produced. Their data is shown below.
Number of widgets, x
35
88
110
135
154
190
Cost per widget, y
9.32
2.63
1.42
1.32
2.12
5.50
(a) Why should a quadratic model be considered for
this data set as opposed to linear or exponential?
(b) Use your calculator to create a scatterplot of this
data to verify its quadratic nature.
COMMON CORE ALGEBRA I, UNIT #10 – STATISTICS – LESSON #8
eMATHINSTRUCTION, RED HOOK, NY 12571, © 2013
Name: ____________________________________
Date: _________________
OTHER TYPES OF REGRESSION
COMMON CORE ALGEBRA I HOMEWORK
FLUENCY
1. For each scatterplot below, determine the best type of regression from: linear, exponential, or quadratic.
Draw a representative curve (line, exponential, or parabola) through the data.
(a)
(b)
Type: ________________
(d)
(c)
Type:__________________
(e)
Type: _______________
Type: _______________
(f)
Type: ________________
Type: _______________
2. Given the scatterplot below, which of the following equations would best mode the data? Explain your
choice.
(1) y  3x  6
(3) y  4 x2  20 x  3
(2) y  6  2 
(4) y  2 x 2  6 x  4
x
COMMON CORE ALGEBRA I, UNIT #10 – STATISTICS – LESSON #8
eMATHINSTRUCTION, RED HOOK, NY 12571, © 2013
APPLICATIONS
3. A marketing company is keeping track of the number of hits that a website receives on a daily basis. Their
data for the first two weeks is shown below. A scatterplot of the data is also shown.
Hits
0
120
3
145
5
162
10
220
14
270
Daily Hit Count for Site
300
Days
200
100
(a) Of the three types of regression we have studied
which seems least likely to fit this data? Explain
your choice.
5
10
15
Days After the Website Launched
(b) Find a linear equation, in the form y  ax  b , that best models this data and an exponential equation, in the
form y  a  b  that best models this data. Round all parameters to the nearest hundredth.
x
Linear Model
Exponential Model
(c) How close are the two model’s outputs when
x  10 ? Show the values you find.
(d) How close are the two model’s outputs when
x  30 ? Show the values that you find.
(e) Which model will predict faster growth of website hits over time? Explain your answer. You may want to
experiment by graphing both models.
COMMON CORE ALGEBRA I, UNIT #10 – STATISTICS – LESSON #8
eMATHINSTRUCTION, RED HOOK, NY 12571, © 2013
1/--pages
Пожаловаться на содержимое документа